Mathematical Analysis, Modelling, and Applications

The activity in mathematical analysis is mainly focussed on ordinary and partial differential equations, on dynamical systems, on the calculus of variations, and on control theory. Connections of these topics with differential geometry are also developed.The activity in mathematical modelling is oriented to subjects for which the main technical tools come from mathematical analysis. The present themes are multiscale analysis, mechanics of materials, micromagnetics, modelling of biological systems, and problems related to control theory.The applications of mathematics developed in this course are related to the numerical analysis of partial differential equations and of control problems. This activity is organized in collaboration with MathLab for the study of problems coming from the real world, from industrial applications, and from complex systems.

Asymptotics as $s \to 0^+$ of the fractional perimeter on Riemannian manifolds

Caselli M, Gennaioli L. Asymptotics as $s \to 0^+$ of the fractional perimeter on Riemannian manifolds.; 2023.

On the Hausdorff Measure of $\mathbbR^n$ with the Euclidean Topology

Bagnara M, Gennaioli L, Leccese GMaria, Luongo E. On the Hausdorff Measure of $\mathbbR^n$ with the Euclidean Topology. Real Analysis Exchange [Internet]. 2023 ;48. Available from: http://dx.doi.org/10.14321/realanalexch.48.1.1649735306

Fourier transform of BV functions, isoperimetry, and discrepancy theory

Beretti T, Gennaioli L. Fourier transform of BV functions, isoperimetry, and discrepancy theory.; 2024.

Existence and blow-up for non-autonomous scalar conservation laws with viscosity

Bianchini S, Leccese GMaria. Existence and blow-up for non-autonomous scalar conservation laws with viscosity. Journal of Mathematical Analysis and Applications [Internet]. 2025 ;542:128761. Available from: https://www.sciencedirect.com/science/article/pii/S0022247X24006838

Dissipative solutions to Hamiltonian systems

Bianchini S, Leccese GMaria. Dissipative solutions to Hamiltonian systems. Kinetic and Related Models. 2024 ;17.

T.B.A.

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Liouville's theorems and universal estimates for elliptic equations on Riemannian manifolds

Read more about Liouville's theorems and universal estimates for elliptic equations on Riemannian manifolds

Dynamics of vortex-patches

The purpose of this course is to study some dynamical properties of weak solutions to Euler equations in simply-connected domains. A focus will be done on vortex patches which are particular weak solutions where the vorticity is the characteristic functions of a bounded domain. The first part of the course will be devoted to the proof Yudovich's Theorem stating the existence and uniqueness of weak solutions.

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A segregated reduced order model of a pressure-based solver for turbulent compressible flows

Zancanaro M, Ngan VEric Brice, Stabile G, Rozza G. A segregated reduced order model of a pressure-based solver for turbulent compressible flows.; 2024.

A hybrid reduced-order model for segregated fluid-structure interaction solvers in an ALE approach at high Reynolds number

Ngan VEric Brice, Stabile G, Mola A, Rozza G. A hybrid reduced-order model for segregated fluid-structure interaction solvers in an ALE approach at high Reynolds number.; 2024.

Mathematics